Editorial Type:
Article
Article Type:
Research Article

Resonance in Optimal Perturbation Evolution. Part I: Two-Layer Eady Model

H. de Vries Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands

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J. D. Opsteegh Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands

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Print Publication:
01 Mar 2007
DOI:
https://doi.org/10.1175/JAS3867.1
Page(s):
673–694
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Abstract

A detailed investigation has been performed of the role of the different growth mechanisms (resonance, potential vorticity unshielding, and normal-mode baroclinic instability) in the evolution of optimal perturbations constructed for a two-layer Eady model and a kinetic energy norm. The two-layer Eady model is obtained by replacing the conventional upper rigid lid by a simple but realistic stratosphere. To make an unambiguous discussion possible, generally applicable techniques have been developed. At the heart of these techniques lies a description of the linear dynamics in terms of a variable number of potential vorticity building blocks (PVBs), which are zonally wavelike, vertically localized sheets of potential vorticity.

If the optimal perturbation is composed of only one PVB, the rapid surface cyclogenesis can be attributed to the growth of the surface PVB (the edge wave), which is excited by the tropospheric PVB via a linear resonance effect. If the optimal perturbation is constructed using multiple PVBs, this simple picture is modified only in the sense that PV unshielding dominates the surface amplification for a short time after initialization. The unshielding mechanism rapidly creates large streamfunction values at the surface, as a result of which the resonance effect is much stronger. A similar resonance effect between the tropospheric PVBs and the tropopause PVB acts negatively on the surface streamfunction amplification. The influence of the stratosphere to the surface development is negligible.

In all cases reported here, the growth due to traditional normal-mode baroclinic instability contributes either negative or only little to the surface development up to the optimization time of two days. It takes at least four days for the flow to become fully dominated by normal-mode growth, thereby confirming that finite-time optimal perturbation growth differs in many aspects fundamentally from asymptotic normal-mode baroclinic instability.

* Current affiliation: Department of Meteorology, University of Reading, Reading, United Kingdom

Corresponding author address: Dr. Hylke de Vries, Department of Meteorology, University of Reading, P.O. Box 243, Earley Gate, RG6 6BB Reading, United Kingdom. Email: h.devries@reading.ac.uk

Abstract

A detailed investigation has been performed of the role of the different growth mechanisms (resonance, potential vorticity unshielding, and normal-mode baroclinic instability) in the evolution of optimal perturbations constructed for a two-layer Eady model and a kinetic energy norm. The two-layer Eady model is obtained by replacing the conventional upper rigid lid by a simple but realistic stratosphere. To make an unambiguous discussion possible, generally applicable techniques have been developed. At the heart of these techniques lies a description of the linear dynamics in terms of a variable number of potential vorticity building blocks (PVBs), which are zonally wavelike, vertically localized sheets of potential vorticity.

If the optimal perturbation is composed of only one PVB, the rapid surface cyclogenesis can be attributed to the growth of the surface PVB (the edge wave), which is excited by the tropospheric PVB via a linear resonance effect. If the optimal perturbation is constructed using multiple PVBs, this simple picture is modified only in the sense that PV unshielding dominates the surface amplification for a short time after initialization. The unshielding mechanism rapidly creates large streamfunction values at the surface, as a result of which the resonance effect is much stronger. A similar resonance effect between the tropospheric PVBs and the tropopause PVB acts negatively on the surface streamfunction amplification. The influence of the stratosphere to the surface development is negligible.

In all cases reported here, the growth due to traditional normal-mode baroclinic instability contributes either negative or only little to the surface development up to the optimization time of two days. It takes at least four days for the flow to become fully dominated by normal-mode growth, thereby confirming that finite-time optimal perturbation growth differs in many aspects fundamentally from asymptotic normal-mode baroclinic instability.

* Current affiliation: Department of Meteorology, University of Reading, Reading, United Kingdom

Corresponding author address: Dr. Hylke de Vries, Department of Meteorology, University of Reading, P.O. Box 243, Earley Gate, RG6 6BB Reading, United Kingdom. Email: h.devries@reading.ac.uk

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